Two uniform solid spheres possessing unequal masses and unequal radii are released from rest at the same height on a rough incline. Provided the spheres roll without slipping,

Step-by-step solution

Let M be the mass and R be the radius of the solid sphere. The equation of motion along the inclined plane is Mg - f = Ma . The torque equation about the center of mass is fR = I . For pure rolling, a = R , which gives f = Ia R^2 . Substituting f in the first equation, we get Mg - Ia R^2 = Ma . a = Mg M + I R^2 For a solid sphere, the moment of inertia is I = 2 5 MR^2 . a = Mg M + 2 5 M = 5 7 g The acceleration of a solid sphere rolling down an incline is independent of its mass and radius. Since both spheres are r